Genetic analysis in humans depends heavily on complex, sophisticated statistical methods, since humans cannot be manipulated like experimental animals. But methods are not static, and our understanding of their strengths and weaknesses keeps evolving. On the other hand, new methods are introduced to the field and become popular, without ever being rigorously tested. In the past this grant has developed new methods for genetic analysis and has tested and characterized those methods in rigorous theoretical analyses, supplemented by realistic computer simulations and applications to analysis of disease data. The proposed research focuses on linkage analysis and segregation analysis, two of the major tools available for understanding complex diseases. Problems and complications will be quantified, and new methods to solve these problems will be developed. Results from this project will assist the genetic analysis of diabetes, one of the common complex diseases with genetic components. Greater understanding of the genetic contributions to these diseases will lead, in turn, to improved counseling, treatment, and prevention. New solutions will be developed and rigorously evaluated for four critical problem areas: I. Gene-gene interactions - their detection via parametric linkage methods. II. Sex differences - in relation to recombination fractions, mutation rates, and imprinting. III. Ascertainment and likelihood - solve complex, practical problems of ascertainment, which can profoundly affect the results of a segregation analysis; and resolve controversial issues of power calculations and multiple tests. IV. Single nucleotide polymorphism (SNP) variants - their detection in complex diseases, including sample size determination. The project will also be flexible and will move rapidly to address new and pressing problems as they arise during the grant period, as this investigator has done successfully in the past.